It should work.  not sure why it does not in your case.  when you have a black screen (no POST) can try clear cmos settings to see if it helps.

Dell Optiplex 7010 Mini Tower i5-2400 (pcliquidations.com)

Well, I tried it and it didn't work...

move blue jumper to adjacent two empty pins that says RTCRST (clear cmos) for 10 sec then move jumper back.  try i5-2400 again.  upload a pic of your i5-2400 if you can.

If the size 2032 CMOS battery is 5+ years old, it should be replaced.  Or test the voltage.

Also, what version of BIOS do you have?